First 10 digits afteer deciaml point of (1+sqrt(3))^2015

def mul( ab1, ab2):
    """(a1 + b1*sqrt(3)) * (a2 + b2*sqrt(3)) """
    a1, b1 = ab1
    a2, b2 = ab2
    return (a1*a2 + 3*b1*b2, a1*b2 + a2*b1)
def square(ab):
    return mul(ab, ab)
def sqrti( n ):
    """integer part of the square root, for long arithmetics"""
    x = 1
    while True:
        x1 = (x + n//x)//2
        x12 = x1*x1
        if x12 <= n and x12 + 2*x1+1 > n:
            return x1
        x = x1
def intpart( ab ):
    #integer part of a+b*sqrt(3)
    # is a + int(sqrt(b*b*3))
    a, b = ab
    return a + sqrti(b*b*3)

def power( ab, n ):
    if n == 0: return (1,0)
    if n == 1: return ab
    ab_n2 = square(power(ab, n // 2))
    if n % 2: return mul(ab_n2, ab)
    else:     return ab_n2
def smul( ab, k):
    a,b=ab
    return (a*k, b*k)
def subtract_int(ab, n):
    a,b=ab
    return (a-n,b)
def decimal_digits( ab, n ):
    x0 = intpart(ab)
    ab = subtract_int(ab, x0)
    digits = []
    while len(digits)!=n:
        ab = smul(ab, 10)
        digit = intpart(ab)
        digits.append(digit)
        ab = subtract_int(ab, digit)
    return x0, digits

N = 2015
num_digits = 10
print ("Calculating (1+sqrt(3))**{N}".format(N=N))
x0, digits = decimal_digits( power( (1,1), N), num_digits )
print ("Integer part:")
print (x0)
print ("Digits after deciaml point")
print ("".join(map(str,digits)))